Add comprehensive project structure documentation and mermaid flowcharts to README

[Copilot]

README lacked detailed project structure and visual diagrams explaining core mechanisms for developers.

Changes

Project Structure Documentation

• Complete directory tree with 20+ files organized by responsibility (Interfaces, Parsers, Operations, Factories, Core Classes)
• Namespace organization showing logical component grouping
• Statistics: ~4,600 LOC, comprehensive test coverage

Mermaid Diagrams (5 total)

• Layered architecture: Client → API → Factory/Core → Interfaces → Parser/Operations
• Component dependencies: Poly → IPolynomialParser/IPolynomialOperation → concrete implementations
• Polynomial creation flow: Sequence diagram of Factory → Parser → TermCollection → Poly instantiation
• Operation execution: How operations transform polynomials without mutation
• Parsing mechanism: Validation → normalization → term extraction → sorting

Developer Guide

• SOLID principles applied with concrete examples (SRP: separate Parser/Operations, OCP: IPolynomialOperation, DIP: Factory accepts IPolynomialParser)
• Design patterns: Factory, Strategy, Command, Template Method with usage examples
• Extension guide: Add custom parsers (LaTeXParser) or operations (SecondDerivativeOperation)
• Performance notes: O(n log n) sorting, no finalizers, immutable operations

Usage Examples

15+ code snippets covering:

• 5 ways to create polynomials (direct, factory, custom parser, from terms)
• Calculus operations (integration, differentiation)
• Root finding and extrema detection
• Custom operation implementation

Additional

• Table of contents, badges, build instructions, contributing guidelines
• Links to existing ARCHITECTURE.md and SOLID_IMPROVEMENTS.md

Example: Extending with Custom Operation

public class SecondDerivativeOperation : IPolynomialOperation<Poly>
{
    public Poly Execute(IPolynomial polynomial)
    {
        var diffOp = new DifferentiationOperation();
        var firstDerivative = diffOp.Execute(polynomial);
        return diffOp.Execute(firstDerivative);
    }
}

README expanded from 66 to 643 lines.

Original prompt

Edit readme file for better explain the project. Also add a comprehensive project structure quide for developers, in detail. The read me should include project structure in detail. It should also include mermaid flowcharts about important mechanisms.

---

✨ Let Copilot coding agent set things up for you — coding agent works faster and does higher quality work when set up for your repo.

[Copilot]

Pull request overview

This PR transforms the README from a basic 66-line document into a comprehensive 643-line developer guide with detailed project structure documentation, architecture diagrams, and extensive usage examples. The documentation provides clear insights into the codebase's SOLID principles implementation and design patterns.

Key Changes

• Added complete project structure tree showing 20+ files organized by responsibility (Interfaces, Parsers, Operations, Factories, Core Classes)
• Created 5 Mermaid diagrams illustrating layered architecture, component dependencies, polynomial creation workflow, operation execution flow, and parsing mechanism
• Expanded usage examples from basic operations to 15+ code snippets covering multiple creation methods, calculus operations, root finding, extrema detection, and custom operation implementation

Reviewed changes

Copilot reviewed 1 out of 2 changed files in this pull request and generated 2 comments.

File	Description
README.md	Complete documentation overhaul with project structure, architecture diagrams, comprehensive usage examples, developer guide with SOLID principles and design patterns, and contributing guidelines
.gitignore	Added pattern to ignore *.backup files

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[Copilot]

The project structure documentation shows Documentation/ as a subdirectory containing ARCHITECTURE.md, SOLID_IMPROVEMENTS.md, and REFACTORING_SUMMARY.md. However, these files are actually located in the root directory of the repository, not in a Documentation/ subdirectory.

Update the structure to reflect the actual location:

├── ARCHITECTURE.md                 # Detailed architecture guide
├── SOLID_IMPROVEMENTS.md           # SOLID principles documentation  
├── REFACTORING_SUMMARY.md          # Refactoring history

Suggested change

	├── Documentation/ # Architecture documentation
	│ ├── ARCHITECTURE.md # Detailed architecture guide
	│ ├── SOLID_IMPROVEMENTS.md # SOLID principles documentation
	│ └── REFACTORING_SUMMARY.md # Refactoring history
	│
	├── ARCHITECTURE.md # Detailed architecture guide
	├── SOLID_IMPROVEMENTS.md # SOLID principles documentation
	├── REFACTORING_SUMMARY.md # Refactoring history

[Copilot]

The example code is incorrect. The Maximum() method returns the maximum value of the polynomial, not the x-coordinate where the maximum occurs. To get the x-coordinate, use the MaxLocation() method instead.

The correct code should be:

var poly = new Poly("x^2 - 4x + 3", -10, 10);

// Find maximum location (x-coordinate)
double maxX = poly.MaxLocation();
double maxValue = poly.Calculate(maxX);
Console.WriteLine($"Maximum at x = {maxX}, value = {maxValue}");

// Find minimum location (x-coordinate)
double minX = poly.MinLocation();
double minValue = poly.Calculate(minX);
Console.WriteLine($"Minimum at x = {minX}, value = {minValue}");

Suggested change

	// Find maximum
	double maxX = poly.Maximum();
	double maxValue = poly.Calculate(maxX);
	Console.WriteLine($"Maximum at x = {maxX}, value = {maxValue}");
	// Find minimum
	double minX = poly.Minimum();
	// Find maximum location (x-coordinate)
	double maxX = poly.MaxLocation();
	double maxValue = poly.Calculate(maxX);
	Console.WriteLine($"Maximum at x = {maxX}, value = {maxValue}");
	// Find minimum location (x-coordinate)
	double minX = poly.MinLocation();